Preheat the oven to 350°F (175°C).
Grease and flour a 9x13 inch baking pan.
In a mixing bowl, whisk together the flour, baking powder, baking soda, and salt.
In a separate bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs, one at a time, mixing well after each addition, then stir in vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the chopped apples gently.
Pour the batter into the prepared pan and smooth the top.
In a separate bowl, combine brown sugar, flour, cinnamon, and butter to make the crumb topping.
Sprinkle the crumb topping evenly over the batter.
Bake for 40-45 minutes or until a toothpick comes out clean.
While the cake cools, prepare the cinnamon apple drizzle by combining powdered sugar, cinnamon, and milk until smooth.
Drizzle the cinnamon apple mixture over the cooled cake.